Finite Group Databasebeta

← #25156721

Subgroups — #25156721

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583111C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic, complemented
3#19137506C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic, complemented
5#19136097C211yesmaximal, characteristic, complemented
6#19136013C211yesmaximal, characteristic, complemented
7#19135831C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic
11#19134946C211yesmaximal, characteristic
12#19134932C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14#19134841C211yesmaximal, characteristic, complemented
15C43×#2448C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583111—24no—
22C4×#10621884—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582770—21no—
38#14582770—21no—
39#14582765C2211yescharacteristic
40#14582758—21no—
41#95×D43—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#124×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#399—21no—
53C43×#397—21no—
54C43×#391C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#388—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884D414yes—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—41no—
80C4×D172—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89#13063258—41no—
90#13063256—22no—
91C4⋊(C43⋊C8)—22no—
92#13063249—22no—
93#13063249—22no—
94#13063249—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—41no—
98#13063245—22no—
99#13063245—22no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43C2311yescharacteristic
106C22×D4×C43C2311yescharacteristic
107#124×C43—22no—
108#124×C43—41no—
109C4×Q8×C43—22no—
110C4×Q8×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43D411yescharacteristic
131#95×C43D411yescharacteristic
132C24×C43—21no—
133C23×D43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43C2×D412yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C2×D412yes—
163C2×D172#4112yes—
164C2×D172#4112yes—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×C4×D43—81no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—81no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—81no—
187C22⋊C4×C43—81no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—42no—
195#10621884—28no—
196#10621882—44no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43#4112yes—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C2×D412yes—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43#13512yes—
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43H(5,𝔽2)11yescharacteristic
275C2×C4×C432−1+411yescharacteristic
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285D172—22no—
286D172—22no—
287D172—22no—
288D172#12314yes—
289C4×D43—84no—
290C4×D43—84no—
291C4×D43—84no—
292C43⋊C8—22no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296#26168—431nomaximal, Sylow
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43#52511yescharacteristic
305C22×C43D4211yescharacteristic
306C22×C43#54811yescharacteristic
307C22×C43C2×#13511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57611yescharacteristic
310C22×C43#57711yescharacteristic
311C2×D43—24no—
312C2×D43—42no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C4×C43—22no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—42no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43C2×#12311yescharacteristic
328C4×C43#53911yescharacteristic
329C4×C43#54711yescharacteristic
330C4×C43#55311yescharacteristic
331Dic43—42no—
332Dic43—81no—
333Dic43—81no—
334C2×#463—431no—
335C2×C4×SD16—431no—
336#2448D4311yescharacteristic, complemented
337#2349—431no—
338#2092—431no—
339#2088—431no—
340#2074—431no—
341#2042—431no—
342#1934—431no—
343#1916—431no—
344#1879—431no—
345#1879—431no—
346#1877—431no—
347#1863—431no—
348#1862—431no—
349C2×C43—161no—
350C2×C43#244311yescharacteristic
351C2×C43#310211yescharacteristic
352C2×C43#311811yescharacteristic
353C2×C43#326811yescharacteristic
354C2×C43#328211yescharacteristic
355C2×C43#336111yescharacteristic
356C2×C43#337611yescharacteristic
357D43—44no—
358C22×SD16—431no—
359C22×D8—431no—
360C2×#124C2×D4311yescharacteristic
361C2×C4×Q8C2×D4311yescharacteristic
362C2×C4×D4—431no—
363C2×C4×D4—431no—
364C2×C4×D4—431no—
365#463—864no—
366C4×SD16—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×C4×C8—431no—
379#399—21no—
380#397—21no—
381#391C2×D4311yescharacteristic
382#390C2×D4311yescharacteristic
383#390C2×D4311yescharacteristic
384#389—431no—
385#389—431no—
386#389C2×D4311yescharacteristic
387#388—21no—
388#388—21no—
389#385—861no—
390#385—861no—
391#382—431no—
392#380—861no—
393C4×C4⋊C4C2×D4311yescharacteristic
394C2×#95—861no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#336—431no—
400#336—431no—
401#336—431no—
402#336—431no—
403C43#2616811yescharacteristic, complemented, Sylow
404C22×Q8C22×D4311yescharacteristic
405C22×D4—431no—
406C22×D4C22×D4311yescharacteristic
407C23×C4—861no—
408C23×C4—861no—
409C23×C4—861no—
410C2×SD16—434no—
411C2×SD16—862no—
412C2×SD16—862no—
413C2×D8—862no—
414C2×D8—862no—
415C2×D8—862no—
416C22×C8—431no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8—431no—
420#124—22no—
421#124—41no—
422C4×Q8—22no—
423C4×Q8—41no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—1721no—
429C4×D4—1721no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C22⋊D4311yescharacteristic
438C2×C4⋊C4C22⋊D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C42—21no—
451C2×C42C22×D4311yescharacteristic
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454#107—1721no—
455#106—862no—
456C4⋊C8—862no—
457#103—862no—
458#103—862no—
459#103—862no—
460#102—862no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—1721no—
465C4×C8—862no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95C22⋊D4311yescharacteristic
474#95C22⋊D4311yescharacteristic
475C24—21no—
476C24—861no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8D4×D4312yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—432no—
490C2×D4—432no—
491C2×D4—432no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—864no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—3441no—
503C22×C4—3441no—
504C22×C4—3441no—
505C22×C4—3441no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517SD16—868no—
518D8—1724no—
519C2×C8—432no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—41no—
537C4⋊C4—42no—
538C4⋊C4—81no—
539C4⋊C4—432no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—3441no—
546C4⋊C4—3441no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—864no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—862no—
571C23—862no—
572C23—862no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23C22×C22⋊D4311yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—434no—
587D4—862no—
588D4—862no—
589D4—862no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—862no—
617C2×C4—3444no—
618C2×C4—3444no—
619C2×C4—3444no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4#1306334512yes—
629C2×C4C2×D4×D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#1306337011yescharacteristic
634C2×C4#1306337211yescharacteristic
635C8—862no—
636C8—1721no—
637C8—1721no—
638C8—1721no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—864no—
647C22—1722no—
648C22—1722no—
649C22—1722no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22#1458340611yescharacteristic
654C22D4×C22⋊D4311yescharacteristic
655C22#1458355611yescharacteristic
656C22C2×#1306334511yescharacteristic
657C22#1458369711yescharacteristic
658C22#1458370211yescharacteristic
659C22#1458370711yescharacteristic
660C4—22no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—3441no—
670C4—3441no—
671C4—1722no—
672C4#123×D4311yescharacteristic
673C4#1458349211yescharacteristic
674C4#1458354711yescharacteristic
675C4#1458359411yescharacteristic
676C2—161no—
677C2—1724no—
678C2#1913832711yescharacteristic
679C2#1914460711yescharacteristic
680C2#1914477311yescharacteristic
681C2#1914613611yescharacteristic
682C2#1914630311yescharacteristic
683C2#1914725111yescharacteristic
684C2#1914741611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2448C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2448D43
hypocenterC43#26168
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2448

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×#10621884C2semidirect
3. #19137506C2semidirect
4. #19136116C2semidirect
5. #19136097C2semidirect
6. #19136013C2semidirect
7. #19135831C2semidirect
8. #19135281C2semidirect
9. #19135154C2semidirect
12. #19134932C2semidirect
13. #19134849C2semidirect
14. #19134841C2semidirect
15. C43×#2448C2semidirect
336. #2448D43semidirect
403. C43#26168semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145831112
C2×C4×#106218842
#191375062
#191361162
#191360972
#191360132
#191358312
#191352812
#191351542
#191349462
#191349322
#191348492
#191348412
C43×#24482
#2616843